Abstract

A radiative transfer model was applied to examine the effects of vertically stratified inherent optical properties of the water column associated with near-surface plumes of suspended particulate matter on spectral remote-sensing reflectance, Rrs(λ), of coastal marine environments. The simulations for nonuniform ocean consisting of two layers with different concentrations of suspended particulate matter (SPM) are compared with simulations for a reference homogeneous ocean whose SPM is identical to the surface SPM of the two-layer cases. The near-surface plumes of particles are shown to exert significant influence on Rrs(λ). The sensitivity of Rrs(λ) to vertical profile of SPM is dependent on the optical beam attenuation coefficient within the top layer, c1(λ), thickness of the top layer, z1, and the ratio of SPM in the underlying layer to that in the top layer, SPM2/SPM1, as well as the wavelength of light, λ. We defined a dimensionless spectral parameter, P(λ)=c1(λ)×z1×(SPM2/SPM1), to quantify and examine the effects of these characteristics of the two-layer profile of SPM on the magnitude and spectral shape of Rrs(λ). In general, the difference of Rrs(λ) between the two-layer and uniform ocean decreases to zero with an increase in P(λ). For the interpretation of ocean color measurements of water column influenced by near-surface plumes of particles, another dimensionless parameter P′(λ) was introduced, which is a product of terms representing homogenous ocean and a change caused by the two-layer structure of SPM. Based on the analysis of this parameter, we found that for the two-layer ocean there is a good relationship between Rrs(λ) in the red and near-infrared spectral regions and the parameters describing the SPM(z) profile, i.e., SPM1, SPM2, and z1.

Figures (10)

Spectra of (a) mass-specific absorption coefficient of particles, ap*(λ), and (b) mass-specific scattering coefficient of particles, bp*(λ), used in this study to generate input inherent optical properties for radiative transfer simulations. As indicated, the data are shown for the mineral-dominated (solid curve), mixed (dashed curve), and organic-dominated (dotted curve) particulate assemblages. The curves in black represent the actual experimental data and the curves in gray represent the best-fit curves to the experimental data or extrapolated portions of the spectra (see text for details).

Example near-surface vertical profiles of the particulate beam attenuation coefficient at 660 nm, cp(660), measured in coastal polar waters of Kongsfjord, Spitsbergen. The time and location of measurements are (i) Station MI210, July 10, 1998; 78°59.9’N, 11°58.6’E. (ii) Station B910, July 10, 1998; 79°8’N, 11°55.1’E. (iii) Station BENT2, July 8, 1998; 78°57.8’N, 11°6.2’E. The inset shows the rescaled plot for the station BENT2.

Left-hand panels: Example results from radiative transfer simulations for spectral remote-sensing reflectance, Rrs(λ), for vertically nonuniform two-layer ocean with SPM1>SPM2 (gray curves) and for a reference uniform ocean with SPM(z)=SPM1 (black curves), where SPM is the mass concentration of suspended particulate matter and the subscripts 1 and 2 denote the top near-surface layer and the underlying layer of the ocean, respectively. Right-hand panels: The percent difference in remote-sensing reflectance, ΔRrs(λ), between the nonuniform and uniform vertical profiles of SPM(z). Each graph for ΔRrs(λ) has been created from corresponding data presented in the left-hand panels. The various plots in each graph correspond to simulations for nonuniform ocean with different values for the thickness of the top near-surface layer, z1. The effect of increasing z1 on the location of the Rrs(λ) spectra is indicated by an arrow. The type of particulate assemblage and the magnitudes of SPM1 and the ratio SPM2/SPM1 are also given.

Example results from radiative transfer simulations that illustrate the variation in the percent difference in remote-sensing reflectance, ΔRrs(λ), between the vertically nonuniform two-layer ocean and uniform ocean as a function of dimensionless parameter P(λ). The results are shown for five light wavelengths (355, 443, 555, 655, and 805 nm) for waters with mineral-dominated (black symbols) and organic-dominated (gray symbols) particulate assemblages and a given ratio SPM2/SPM1=0.1. Each plot (i.e., a series of data points depicted by the same symbol) in a given graph consists of a number of data points that correspond to simulations for different values of z1. For the sake of clarity, a few example sets of data points at 665 nm extracted from Fig. 4(d) are shown in Fig. 4(f) to aid in the visualization of the effects of varying z1 and SPM1 on ΔRrs(λ).

Example results from radiative transfer simulations showing the variation in beam attenuation coefficient within the top near-surface oceanic layer, c1(λ), as a function of mass concentration of suspended particulate matter within that layer, SPM1, for five light wavelengths as indicated.

Example results from radiative transfer simulations showing the variation in the threshold thickness of the top near-surface oceanic layer, z1max, as a function of the beam attenuation coefficient within that layer, c1, for five light wavelengths, 355, 443, 555, 665, and 805 nm.

Example results from radiative transfer simulations showing the variation in the threshold thickness of the top near-surface oceanic layer, z1max, as a function of light wavelength, λ, for waters with mineral-dominated (panel a) and organic-dominated (panel b) particulate assemblages. The results were obtained for vertically nonuniform two-layer ocean with a given ratio SPM2/SPM1=0.1 and for different values of SPM1 as indicated.

Example results from radiative transfer simulations showing the variation in light wavelength, λmax, as a function of the thickness of the top near-surface layer of the vertically nonuniform two-layer ocean, z1, for different values of particle concentration within that top layer, SPM1, as indicated. The ratio SPM2/SPM1 is 0.1 and the particulate assemblage is mineral-dominated for the presented simulations. The value of λmax represents the light wavelength at which the absolute percent difference in spectral remote-sensing reflectance, |ΔRrs(λ)|, reaches its maximum for a given pair of simulations of vertically nonuniform and uniform ocean.

Data obtained with radiative transfer simulations and the associated fitted curves that show the relationship between the remote-sensing reflectance for vertically nonuniform two-layer ocean, Rrs-non(λ), and the dimensionless parameter, P′(λ), at four example light wavelengths (655, 705, 805, and 855 nm) from the red-NIR portion of the spectrum. The results represent all simulations made in this study for which the absolute percent difference in remote-sensing reflectance between the nonuniform and uniform cases, |ΔRrs(λ)|, was greater or equal to 5%. The number of data points, N, included in each graph is given.

Optimized spectral values of best-fit coefficients, A(λ), B(λ), C(λ), and D(λ), for the relationship between the remote-sensing reflectance of vertically nonuniform two-layer ocean, Rrs-non(λ), and the parameter P′(λ) in the red-NIR spectral region.

Table 2. Parameters of the Vertical Profile of Mass Concentration of Suspended Particulate Matter, SPM(z), Considered in Radiative Transfer Simulations of a Two-Layer Ocean for Each of the Three Composition Types of Particulate Assemblages, i.e., Mineral-Dominated, Mixed, and Organic-Dominateda

a The equations of the fitted functions are given along with the spectral range used in the fit. The root mean square error (RMSE) was calculated as RMSE=(∑i=1N(Xmi−Xfi)2)/n, where Xm refers to the measured value of ap* or bp*, Xf refers to the fitted value of ap* or bp*, i stands for the ith wavelength of light, and n is the total number of measured spectral data points used for fitting. Note that for ap*(λ) only the long-wavelength portion of the spectrum was used to determine the best-fit function. At shorter wavelengths the actual experimental data of ap*(λ) were used.

Table 2.

Parameters of the Vertical Profile of Mass Concentration of Suspended Particulate Matter, SPM(z), Considered in Radiative Transfer Simulations of a Two-Layer Ocean for Each of the Three Composition Types of Particulate Assemblages, i.e., Mineral-Dominated, Mixed, and Organic-Dominateda

SPM1(gm−3)

SPM2(gm−3)

z1(m)

Number of Simulations

0.5

0.05

0.1–1 (step 0.1)

1–5 (0.5)

5–10 (1)

10–20 (5)

75

0.1

0.25

1

0.1

0.1–1 (0.1)

1–5 (0.5)

5–10 (1)

10–15 (5)

72

0.2

0.5

5

0.5

0.1–1 (0.1)

1–5 (0.5)

5–6 (1)

57

1

2.5

10

1

0.1–1 (0.1)

1–4 (0.5)

48

2

5

25

2.5

0.1–1 (0.1)

1–2 (0.5)

36

5

12.5

50

5

0.1–1 (0.1)

30

10

25

aSPM1 is the mass concentration of particles within the top near-surface layer, SPM2 is the particle concentration within the underlying layer, and z1 is the thickness of the top layer. The range of z1 and the step for z1, which were varied from one simulation to another, are given. The number of simulations for each value of SPM1 is also given.

Tables (2)

Table 1.

Best-Fit Functions and the Root Mean Square Error for the Spectra of Mass-Specific Absorption, ap*(λ), and Scattering, bp*(λ), Coefficients of Suspended Particlesa

a The equations of the fitted functions are given along with the spectral range used in the fit. The root mean square error (RMSE) was calculated as RMSE=(∑i=1N(Xmi−Xfi)2)/n, where Xm refers to the measured value of ap* or bp*, Xf refers to the fitted value of ap* or bp*, i stands for the ith wavelength of light, and n is the total number of measured spectral data points used for fitting. Note that for ap*(λ) only the long-wavelength portion of the spectrum was used to determine the best-fit function. At shorter wavelengths the actual experimental data of ap*(λ) were used.

Table 2.

Parameters of the Vertical Profile of Mass Concentration of Suspended Particulate Matter, SPM(z), Considered in Radiative Transfer Simulations of a Two-Layer Ocean for Each of the Three Composition Types of Particulate Assemblages, i.e., Mineral-Dominated, Mixed, and Organic-Dominateda

SPM1(gm−3)

SPM2(gm−3)

z1(m)

Number of Simulations

0.5

0.05

0.1–1 (step 0.1)

1–5 (0.5)

5–10 (1)

10–20 (5)

75

0.1

0.25

1

0.1

0.1–1 (0.1)

1–5 (0.5)

5–10 (1)

10–15 (5)

72

0.2

0.5

5

0.5

0.1–1 (0.1)

1–5 (0.5)

5–6 (1)

57

1

2.5

10

1

0.1–1 (0.1)

1–4 (0.5)

48

2

5

25

2.5

0.1–1 (0.1)

1–2 (0.5)

36

5

12.5

50

5

0.1–1 (0.1)

30

10

25

aSPM1 is the mass concentration of particles within the top near-surface layer, SPM2 is the particle concentration within the underlying layer, and z1 is the thickness of the top layer. The range of z1 and the step for z1, which were varied from one simulation to another, are given. The number of simulations for each value of SPM1 is also given.